If you recall, a dependent T-test compares the differences in means of data with identical sample sizes before and after treatment – our data being the earnings of a slot machine and the treatment being a change in settings.

An independent T-test allows us to compare data sets with different numbers of samples to determine if they are statistically different.

Here’s an example:

A casino has 2 slot zones, Zone 1, with 5 machines and Zone 2, with 10 machines. We want to find out if one area is earning more than another.

Divide the pooled variance by the respective sample sizes of the 2 zones, add the result and finally square root that.

(9.15 / 5) + (9.15/10) = 1.83 + 0.92 = 2.75

Square Root 2.75 = 1.657

Step 5:

Now, we take the difference of the means for Zone 1 and 2 and divide it by 1.657. This is known as your T-statistic.

T = 14.80 – 12.40 / 1.657 = 2.40 / 1.657 = 1.448267583 or 1.448

Step 6 (Finally):

Compare the T-statistic with the T-table. Looking at this table, we get our degrees of freedom, or df, by subtracting 2 from 5+10 = 13. Now, we will find our T-statistic on this table.

We see that our T-statistic of 1.448 is between 90% – 95% on a one-tailed test. This means that we are between 90% – 95% sure that from this sample data, Zone 1’s earnings are higher than Zone 2’s earnings.